2011年4月
Nonlinear Wave Equation for Ultrasound Beam in Nonuniform Bubbly Liquids
Journal of Fluid Science and Technology
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回数 : 80
- ,
- ,
- ,
- 巻
- 6
- 号
- 2
- 開始ページ
- 279
- 終了ページ
- 290
- 記述言語
- 日本語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1299/jfst.6.279
- 出版者・発行元
- 社団法人 日本機械学会
In our previous paper (Kanagawa et al., J. Fluid Sci. Tech., 5, 2010), we have proposed a systematic method for derivation of various types of nonlinear wave equations for plane waves in bubbly liquids. The method makes use of an asymptotic expansion with multiple scales in terms of a small wave amplitude as an expansion parameter and a set of scaling relations of physical parameters, based on basic equations of two-fluid model of bubbly flows. In this paper, we extend the method so as to handle a weakly diffracted ultrasound beam in a quiescent liquid containing a number of spherical gas bubbles distributed with a weak nonuniformity. Because of the high expandability of the original method, the extension can be accomplished by adding a scaling relation of the diameter of the beam to the original set of scaling relations. As a result, we derive a generalized Khokhlov—Zabolotskaya—Kuznetsov (KZK) equation [or a generalized Kadomtsev—Petviashvili (KP) equation] for a long wave and low frequency case.
- リンク情報
- ID情報
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- DOI : 10.1299/jfst.6.279
- ISSN : 1880-5558
- CiNii Articles ID : 130000664748